Firstly congratualtions on finding enough work to be on the road a lot.
I don't think taking the kids along all the time would be good for them if it is permanent like you say. A few trips for the experience now and then but a permanent fixture does not sound good for the band or kids.
If all the band feel the same I would suggest mentioning to the parents that you all feel the same, it might make them realise that it is not the best solution.